Nonlinear magnetoelastostatics: Energy functionals and their second variations

被引：6

作者：

Bustamante, Roger ^{[1
]}

Ogden, Ray W. ^{[2
]}

机构：

[1] Univ Chile, Dept Ingn Mecan, Santiago, Chile

[2] Univ Aberdeen, Sch Engn, Aberdeen AB9 1FX, Scotland

来源：

MATHEMATICS AND MECHANICS OF SOLIDS | 2013年 / 18卷 / 07期

关键词：

Magnetoelasticity; variational formulations; second variation; free space; energy function;

D O I：

10.1177/1081286512448347

中图分类号：

T [工业技术];

学科分类号：

08 ;

摘要：

Two variational principles for nonlinear magnetoelastostatics are studied, considering a magnetosensitive body completely surrounded by free space extending to infinity. The functionals depend on the deformation function as one of the independent variables, and on either the scalar magnetic potential or the magnetic vector potential as the independent magnetic variable. Alternative representations for the energy densities are given for free space, from which simple expressions for the first and second variations of the functionals are obtained.

引用

收藏

页码：760 / 772

页数：13

相关论文

共 21 条

[1] QUASICONVEXITY AT THE BOUNDARY, POSITIVITY OF THE 2ND VARIATION AND ELASTIC STABILITY [J].

BALL, JM ;

MARSDEN, JE .

ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 1984, 86 (03) :251-277

[2] Magnetoelasticity of highly deformable thin films: Theory and simulation [J].

Barham, M. ;

Steigmann, D. J. ;

White, D. .

INTERNATIONAL JOURNAL OF NON-LINEAR MECHANICS, 2012, 47 (02) :185-196

[3] Limit-point instability of a magnetoelastic membrane in a stationary magnetic field [J].

Barham, M. ;

Steigmann, D. J. ;

McElfresh, M. ;

Rudd, R. E. .

SMART MATERIALS & STRUCTURES, 2008, 17 (05)

[4]

Brown W. F., 1966, Magnetoelastic interactions

[5] On Variational Formulations in Nonlinear Magnetoelastostatics [J].

Bustamante, R. ;

Dorfmann, A. ;

Ogden, R. W. .

MATHEMATICS AND MECHANICS OF SOLIDS, 2008, 13 (08) :725-745

[6] A nonlinear magnetoelastic tube under extension and inflation in an axial magnetic field: numerical solution [J].

Bustamante, R. ;

Dorfmann, A. ;

Ogden, R. W. .

JOURNAL OF ENGINEERING MATHEMATICS, 2007, 59 (01) :139-153

[7] Numerical solution of finite geometry boundary-value problems in nonlinear magnetoelasticity [J].

Bustamante, R. ;

Dorfmann, A. ;

Ogden, R. W. .

INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES, 2011, 48 (06) :874-883

[8] Some problems in nonlinear magnetoelasticity [J].

Dorfmann, A ;

Ogden, RW .

ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK, 2005, 56 (04) :718-745

[9] Nonlinear magnetoelastic deformations [J].

Dorfmann, A ;

Ogden, RW .

QUARTERLY JOURNAL OF MECHANICS AND APPLIED MATHEMATICS, 2004, 57 :599-622

[10]

Holzapfel G., 2000, Nonlinear Solid Mechanics: A Continuum Approach forEnineering